Actually, I have a lot of experience with this! (family in Detroit.) It definitely will take longer than you want. Don't plan on one long stop, like a long meal - instead, plan on several shorter stops. Bring toys she hasn't seen before - just small stuff, and hand it out when the kids get antsy. I used to have a child tray that I got at a baby store that was nice at that age - they could color and put their crayons on the tray, which sat over the car seat arms. Magnadoodle is also good for the car.
Bring lots of kid music and read books (bring a book light if you're traveling after dark.) Sing and tell stories. If she watches TV, think about a portable DVD player. Loony Tunes shorts are perfect for the car, and they come in a boxed set. Anything short seems to be good - we have a lot of old cartoons that we watch in the car. Wallace and Grommit shorts, too. If you're traveling during the day you can play simple games like I spy or "who can find a car that's red" to distract them for a few minutes.
Avoid junk food and sugar - it just makes everyone feel bloated and cranky. Bring some healthy snacks for the car, like fresh fruit, cheese, crackers. Bring bottled water, because in cold weather the inside of a car after a long trip gets really dry.
In my experience, going at bedtime has mixed results - sometimes we just arrive at midnight with very tired kids who just fell asleep at 11, and then you don't enjoy the whole next day (because everyone is so tired and cranky.) So I wouldn't worry too much about not being able to travel at bedtime. Good luck!